Which of the following ionisation energy valuyes for calcium show a sudden increase?

Options

A. Third
B. Second
C. First
D. Fourth

Explanation

To determine which ionization energy value for calcium shows a sudden increase, we need to analyze the electronic configuration of calcium and understand how ionization energies change as we remove electrons.

### Step-by-Step Solution:

1. **Understand Ionization Energy**:
Ionization energy is the energy required to remove an electron from an atom in its gaseous state. The first ionization energy involves removing the outermost electron, while subsequent ionization energies involve removing electrons from increasingly positive ions.

2. **Identify the Electronic Configuration of Calcium**:
Calcium (Ca) has an atomic number of 20. Its electronic configuration is:
\[ \text{Ca: } 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 \]
This means that calcium has two electrons in the 4s subshell, which is the outermost shell.

3. **First Ionization Energy**:
When we remove the first electron from calcium, we remove one of the 4s electrons:
\[ \text{Ca} \rightarrow \text{Ca}^+ + e^- \]
The electronic configuration of \(\text{Ca}^+\) becomes:
\[ 1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 \]

4. **Second Ionization Energy**:
For the second ionization energy, we remove the second 4s electron:
\[ \text{Ca}^+ \rightarrow \text{Ca}^{2+} + e^- \]
The electronic configuration of \(\text{Ca}^{2+}\) becomes:
\[ 1s^2 2s^2 2p^6 3s^2 3p^6 (4s^0) \]

5. **Third Ionization Energy**:
Now, we need to remove an electron from the 3p subshell:
\[ \text{Ca}^{2+} \rightarrow \text{Ca}^{3+} + e^- \]
The electronic configuration of \(\text{Ca}^{3+}\) becomes:
\[ 1s^2 2s^2 2p^6 3s^2 3p^5 \]

6. **Identify Sudden Increase**:
The key point here is that the 3p subshell is fully filled with 6 electrons before the third ionization. Removing an electron from a fully filled subshell (3p) requires significantly more energy due to its stability. Therefore, the third ionization energy will show a sudden increase compared to the second ionization energy.

7. **Conclusion**:
The third ionization energy of calcium shows a sudden increase due to the removal of an electron from a fully filled 3p subshell.

### Final Answer:
The third ionization energy of calcium shows a sudden increase.